Recursive and Explicit Equations

Does this recursive routine model growth or decay?
U₁ = 1000
U_n+1 = U_n*1.25

• Decay

• Growth

What is the explicit rule for the sequence:
11, 22, 44, 88...

• a_n = 2(11)^n-1

• a_n = 11x2

• a_n = 11(2)^n-1

• a_n+1 = a_{n *} 2;  a₁ = 11

Write the explicit rule in recursive form:  f_n = 11(2)^n-1

• f_n=f_{n-1 *} 11 ; f₁=2

• f_n=f_{n-1 *} 2 ; f₁=11

The recursive formula is used to find the next value in a sequence of numbers.

• True

• False

• 1

• 2

• 3

• 4

What is the recursive rule for the sequence:
-2, 12, -72, 432, ...

• a_n = -2(-6)^n-1
  a₁=-2

• a_n =a_n-1 + 10
  a₁=-2

• a_n = -6⋅a_n-1 a₁=-2

• a_n = a_(n-1) - 6 a₁=-2

Write a recursive rule for the sequence 1, 2, 5, 14, 41, 122, …

• a_n = (a_n-1)² + 1

• a_n = 2 a_n-1 - 2

• a_n = 3 a_n-1 - 1

• a_n = 3 a_n-1 + 1

Does this recursive routine model growth or decay, and by what percent?
U₁ = 10
U_n+1 = U_n*.75

• Growth, 75%

• Growth, 25%

• Decay, 75%

• Decay, 25%

Which of the following equations is recursive?

• f(n) = 3n+2

• f(n) = f(n-1) + 3

Which of the following equations is explicit?

• f(n) = 4n + 5

• f(n) = f(n-1) x 5